Problem: Integrate. $\int\left(4e^x-\dfrac5x \right)dx=\,?$ Choose 1 answer: Choose 1 answer: (Choice A) A $4e^x-5\ln|x|+C$ (Choice B) B $4e^x-5+C$ (Choice C) C $e^x-5\ln|x|+C$ (Choice D) D $e^x-5+C$
Solution: We can integrate using the following formulas for the indefinite integrals of $e^x$ and $\dfrac1x$ : $\begin{aligned} &\int e^x\,dx=e^x+C \\\\ &\int \dfrac1x\,dx=\ln|x|+C \end{aligned}$ $\begin{aligned} &\phantom{=}\int\left(4e^x-\dfrac5x \right)dx \\\\ &=4\int e^x\,dx-5\int\dfrac1x \,dx \\\\ &=4e^x-5\ln|x|+C \end{aligned}$